## Friday, September 12, 2008

### 1529

1529 = 11 x 139.

The square of 1529 is the sum of two or more consecutive squares: 15292 = 2337841.

1529 is the number of primitive subsequences of {1, 2, 3, . . . 16, 17}.

1529 is the sum of a positive square and a positive cube in more than one way.

1529 is the 11th term in a sequence defined by the following bilinear recurrence:
Sn+4 Sn = Sn+3 Sn+1 + S2n+2 (n = 1, 2, . . . ) with the initial condition S1 = S2= S3= S4= 1.

This sequence begins 1, 1, 1, 1, 2, 3, 7, 23, 59, 314,
1529, 8209, 833313, 620297, 7869898, . . . .

Interestingly, all the terms are integers even though calculating
Sn+4 a priori involves dividing by Sn. This sequence was discovered by Michael Somos and is associated with the arithmetic of elliptic curves.

1529 18th Street, N.W., is the address of the Mathematical Association of America in Washington, D.C.

Source: Everest, E., S. Stevens, D. Tamsett, and T. Ward. Preprint (Feb. 1, 2008). Primes generated by recurrence sequences.